yaworsw/euler-manager

---
:id: 241
:name: Perfection Quotients
:url: https://projecteuler.net/problem=241
:content: "For a positive integer <var>n</var>, let σ(<var>n</var>) be the sum of
  all divisors of <var>n</var>, so e.g. σ(6) = 1 + 2 + 3 + 6 = 12.\n\nA perfect number,
  as you probably know, is a number with σ(<var>n</var>) = 2<var>n</var>.\n\n| Let
  us define the **perfection quotient** of a positive integer as | <var>p</var>(<var>n</var>)
  | =&nbsp; | \nσ(<var>n</var>)  \n<var>n</var>\n | . |\n\nFind the sum of all positive
  integers <var>n</var> ≤ 10<sup>18</sup> for which <var>p</var>(<var>n</var>) has
  the form <var>k</var> + <sup>1</sup>⁄<sub>2</sub>, where <var>k</var> is an integer.\n\n"